Prog. Theor. Phys. Vol. 43 No. 3 (1970) pp. 808-829
Some Mathematical Aspects of Multiple Poles in the Off-Shell Scattering Amplitude
Institute of Physics, College of General Education, University of Tokyo, Meguro-ku, Tokyo
(Received October 4, 1969)
An attempt at a general theory of the Bethe-Salpeter equation in a previous work is continued, with our attention focussed on the problem of multiple poles in the off-shell scattering amplitude. Basic assumptions made in the previous work reduce the problem to that of multiple poles in the resolvent of a compact operator, which is hermitian analytic as an operator-valued function of P4. Properties of compact operators are discussed on the basis of the Riesz-Schauder theory. Multiple poles are characteristic of non-normal operators, which are shown to be considerably different from hermitian operators in many points of physical importance. Several quantities useful for the understanding of multiple poles are introduced that their properties are investigated. Multiple poles in the resolvent of an analytic operator are studied as a limit of degeneracy of several simple poles.
DOI : 10.1143/PTP.43.808
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Citing Article(s) :
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